If f x - x -2- and g x -fof x - then for x -20- g - x is equal to-A- 1B- 2C- 3D- 0

The correct option is A 1 We have f(x) = |x 2| = x 2,x≥ 2 (x 2),x≤ 2 ∵ x gt; 20,∴ f(x) = x 2 ∴ g(x) = fof(x) = ff(x) = f(x 2) = x 2 2 = x 4 ∴ g'(x) = 1 ...

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Standard XI

Mathematics

Rational Function

If f x =| x -...

Question

If f(x)=|x-2| and g(x) =fof(x), then for x>20, g'(x) is equal to.

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Solution

The correct option is B
1

We have f(x) = |x-2| = ${\begin{matrix} x - 2, x \geq 2 - (x - 2), x \leq 2 \end{matrix}$

$∵ x > 20, ∴ f (x)$ = x-2

$∴ g (x)$ = fof(x) = f{f(x)} = f(x-2) = x-2-2 = x - 4

$∴ g^{'} (x)$ = 1

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If f(x)=|x-2| and g(x) =fof(x), then for x>20, g'(x) is equal to.

The correct option is B 1 We have f(x) = |x-2| = {x−2,x≥2−(x−2),x≤2 ∵x>20,∴f(x) = x-2 ∴g(x) = fof(x) = f{f(x)} = f(x-2) = x-2-2 = x - 4 ∴g′(x) = 1

The correct option is B
1

We have f(x) = |x-2| = ${\begin{matrix} x - 2, x \geq 2 - (x - 2), x \leq 2 \end{matrix}$

$∵ x > 20, ∴ f (x)$ = x-2

$∴ g (x)$ = fof(x) = f{f(x)} = f(x-2) = x-2-2 = x - 4

$∴ g^{'} (x)$ = 1